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Proving irrationality

  1. Oct 30, 2008 #1


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    1. The problem statement, all variables and given/known data

    decide if sqrt2 + sqrt5 +sqrt7 is rational or irrational, with proof

    2. Relevant equations

    3. The attempt at a solution
    i assumed that it was rational, the equation =r
    sqrt2 + sqrt 5=r- sqrt7
    7 + 2sqrt10=r^2 + 7 -2r*sqrt7
    2sqrt10=r^2 -2r*sqrt7
    could i have a hint on how to rearrange this, i have already proved in an earlier question that sqrt2, sqrt5, sqrt7 are irrational

  2. jcsd
  3. Oct 30, 2008 #2


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    Staff Emeritus
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    Gold Member

    You're almost there. square both sides again, and you can write sqrt(7) as a linear combination of rational numbers. i.e. you've shown sqrt(7) is rational.
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